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In conventional SISO fuzzy expert systems (n-element input, m-element output), the implication step requires the O(n×m) operations using compositional rule-based inference (CRI) and individual rule-based inference (IRI). However, this introduces excessive complexity. This paper proposes two methods, sort compositional rule-based inference (SCRI) and sort individual rule-based inference (SIRI) aiming at reducing both temporal and spatial complexity by changing the operation of the implication step to O((n+m)log2(n+m)). We also propose a divide-and-conquer technique, called Quicksort, to verify the accuracy of SCRI and SIRI algorithms deployment to easily outperform the CRI and IRI methods

Reducing Computational Overhead by Improving the CRI and IRI Implication Step